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1. Post‐selection inference for changepoint detection algorithms with application to copy number variation data

   https://doi.org/10.1111/biom.13422  

   Hyun, Sangwon ; Lin, Kevin Z. ; G'Sell, Max ; Tibshirani, Ryan J. ( January 2021 , Biometrics)

   Changepoint detection methods are used in many areas of science and engineering, for example, in the analysis of copy number variation data to detect abnormalities in copy numbers along the genome. Despite the broad array of available tools, methodology for quantifying our uncertainty in the strength (or the presence) of given changepointspost‐selectionare lacking. Post‐selection inference offers a framework to fill this gap, but the most straightforward application of these methods results in low‐powered hypothesis tests and leaves open several important questions about practical usability. In this work, we carefully tailor post‐selection inference methods toward changepoint detection, focusing on copy number variation data. To accomplish this, we study commonly used changepoint algorithms: binary segmentation, as well as two of its most popular variants, wild and circular, and the fused lasso. We implement some of the latest developments in post‐selection inference theory, mainly auxiliary randomization. This improves the power, which requires implementations of Markov chain Monte Carlo algorithms (importance sampling and hit‐and‐run sampling) to carry out our tests. We also provide recommendations for improving practical useability, detailed simulations, and example analyses on array comparative genomic hybridization as well as sequencing data.
2. Privacy-Preserving Policy Synthesis in Markov Decision Processes

   https://doi.org/10.1109/CDC42340.2020.9304015  

   Gohari, Parham ; Hale, Matthew ; Topcu, Ufuk ( December 2020 , Proceedings of the 2020 59th IEEE Conference on Decision and Control (CDC))

   In decision-making problems, the actions of an agent may reveal sensitive information that drives its decisions. For instance, a corporation’s investment decisions may reveal its sensitive knowledge about market dynamics. To prevent this type of information leakage, we introduce a policy synthesis algorithm that protects the privacy of the transition probabilities in a Markov decision process. We use differential privacy as the mathematical definition of privacy. The algorithm first perturbs the transition probabilities using a mechanism that provides differential privacy. Then, based on the privatized transition probabilities, we synthesize a policy using dynamic programming. Our main contribution is to bound the "cost of privacy," i.e., the difference between the expected total rewards with privacy and the expected total rewards without privacy. We also show that computing the cost of privacy has time complexity that is polynomial in the parameters of the problem. Moreover, we establish that the cost of privacy increases with the strength of differential privacy protections, and we quantify this increase. Finally, numerical experiments on two example environments validate the established relationship between the cost of privacy and the strength of data privacy protections.
3. Bayesian sequential monitoring of density estimates

   https://doi.org/10.1002/qre.3050  

   Shamp, Wright ; Linero, Antonio ; Chicken, Eric ( December 2021 , Quality and Reliability Engineering International)

   In this paper, we consider sequentially estimating the density of univariate data. We utilize Pólya trees to develop a statistical process control (SPC) methodology. Our proposed methodology monitors the distribution of the sequentially observed data and detects when the generating density differs from an in‐control standard. We also propose an approximation that merges the probability mass of multiple possible changepoints to curb computational complexity while maintaining the accuracy of the monitoring procedure. We show in simulation experiments that our approach is capable of quickly detecting when a changepoint has occurred while controlling the number of false alarms, and performs well relative to competing methods. We then use our methodology to detect changepoints in high‐frequency foreign exchange (Forex) return data.
4. Bayesian approach for predicting photogrammetric uncertainty in morphometric measurements derived from drones

   https://doi.org/10.3354/meps13814  

   Bierlich, KC ; Schick, RS ; Hewitt, J ; Dale, J ; Goldbogen, JA ; Friedlaender, AS ; Johnston, DW ( September 2021 , Marine Ecology Progress Series)

   Increasingly, drone-based photogrammetry has been used to measure size and body condition changes in marine megafauna. A broad range of platforms, sensors, and altimeters are being applied for these purposes, but there is no unified way to predict photogrammetric uncertainty across this methodological spectrum. As such, it is difficult to make robust comparisons across studies, disrupting collaborations amongst researchers using platforms with varying levels of measurement accuracy. Here we built off previous studies quantifying uncertainty and used an experimental approach to train a Bayesian statistical model using a known-sized object floating at the water’s surface to quantify how measurement error scales with altitude for several different drones equipped with different cameras, focal length lenses, and altimeters. We then applied the fitted model to predict the length distributions and estimate age classes of unknown-sized humpback whales Megaptera novaeangliae , as well as to predict the population-level morphological relationship between rostrum to blowhole distance and total body length of Antarctic minke whales Balaenoptera bonaerensis . This statistical framework jointly estimates errors from altitude and length measurements from multiple observations and accounts for altitudes measured with both barometers and laser altimeters while incorporating errors specific to each. This Bayesian model outputs a posteriormore »predictive distribution of measurement uncertainty around length measurements and allows for the construction of highest posterior density intervals to define measurement uncertainty, which allows one to make probabilistic statements and stronger inferences pertaining to morphometric features critical for understanding life history patterns and potential impacts from anthropogenically altered habitats.« less
5. A Permutation-Based Changepoint Technique for Monitoring Effect Sizes

   https://doi.org/10.1017/pan.2020.44  

   Kent, Daniel ; Wilson, James D. ; Cranmer, Skyler J. ( January 2021 , Political Analysis)

   Abstract Across the social sciences, scholars regularly pool effects over substantial periods of time, a practice that produces faulty inferences if the underlying data generating process is dynamic. To help researchers better perform principled analyses of time-varying processes, we develop a two-stage procedure based upon techniques for permutation testing and statistical process monitoring. Given time series cross-sectional data, we break the role of time through permutation inference and produce a null distribution that reflects a time-invariant data generating process. The null distribution then serves as a stable reference point, enabling the detection of effect changepoints. In Monte Carlo simulations, our randomization technique outperforms alternatives for changepoint analysis. A particular benefit of our method is that, by establishing the bounds for time-invariant effects before interacting with actual estimates, it is able to differentiate stochastic fluctuations from genuine changes. We demonstrate the method’s utility by applying it to a popular study on the relationship between alliances and the initiation of militarized interstate disputes. The example illustrates how the technique can help researchers make inferences about where changes occur in dynamic relationships and ask important questions about such changes.